Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields

[摘要] As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere (J. Comput. Phys. 223 (2007) 846-864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = lambda a to the reaction field induced by the ionic solvent, provided that u = lambda a < 1 where), is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10(-4) relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3-4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-10

[关键词] method of images;fast multipole method;reaction field;ionic solvent;electrostatic interaction;hybrid solvent model